Ingrid Loyau-Kennett, 48, jumped off the bus she was riding in southeast London Wednesday when she saw the man slumped on the sidewalk next to a crashed car.

British police said on Thursday that officers from London’s counter-terrorism unit were heading up the investigation. Eyewitness reports suggest the killing may have been carried out as a protest against British military actions in Muslim countries based on what they say they heard from the alleged attackers.

Loyau-Kennett had intended to offer first aid, but instead found herself standing in the aftermath of the horrific killing of a soldier in broad daylight in Woolwich, London.

“I saw a man on the road obviously injured and a car badly crashed," she told U.K. channel ITV on Thursday. "So I assumed it was a road accident."

However, she says when she got closer she saw a man covered in blood and carrying a butcher's knife. She also says she saw a handgun.

"I thought 'what the heck has happened there?'" she said.

“He was obviously a bit excited and the thing was to talk to him,” Loyau-Kennett said, adding that her instinct was to keep the suspected attacker calm in order to protect the crowd that was beginning to gather.

ITV News

A suspect, left, talks to the camera immediately after Wednesday's attack.

Pictures at the scene show her, hands in pockets, speaking apparently calmly to a man holding a long knife.

Loyau-Kennett, from Cornwall, England, found it “daunting” to continue to engage the blood-soaked man as more bystanders appeared, in particular mothers with their children.

“There were more and more mothers with children coming by so it was more and more important that I talk to him,” she said.

British Prime Minister David Cameron paid tribute to her Thursday, saying she was "brave" as he pledged that U.K. investigators "will not rest until we know every single detail of what happened and we've brought all of those responsible to justice."

"One of the best ways of defeating terrorism is to go about our normal lives. And that is what we shall all do."

A second alleged attacker, his hands covered in blood and holding a meat cleaver, was captured on video -- obtained exclusively by NBC News's U.K. news partner, ITV News -- telling passers-by: "By Allah we swear by the almighty Allah and we will never stop fighting you until you leave us alone."

Eyewitnesses described the victim of the attack as being chopped up like a "piece of meat."

Two suspects allegedly brutally murdered a young soldier in London Monday with large knives as terrified witnesses looked on. Top British security officials are calling the murder a terrorist attack. NBC's Michelle Kosinski reports.

The witnesses said two men were later shot by officers. The injured duo were taken to a hospital where they were later arrested in connection with the case.

NBC News understands the two suspects have been investigated by British security services in the past.

Two further arrests were made Thursday, Britain's Counter Terrorism Command announced. A 29-year-old man and a 29-year-old woman were taken into custody on suspicion of conspiracy to commit murder.

In his statement to reporters on Thursday, Cameron said: "This was not just an attack on Britain - and on our British way of life - it was also a betrayal of Islam - and of the Muslim communities who give so much to our country. There is nothing in Islam that justifies this truly dreadful act."

President Obama released a statement on the attack Thursday, condemning it "in the strongest terms."

"The United States stands resolute with the United Kingdom, our ally and friend, against violent extremism and terror. There can be absolutely no justification for such acts, and our thoughts and prayers are with the family of the victim, the police and security services responding to this horrific act and the communities they serve, and the British people," the president said in the statement.

"Our special relationship with the United Kingdom is especially important during times of trial."